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Abstract

The linear polarization and intensity of a 22° halo has been measured simultaneously at seven wavelengths as of scattering angle. The polarization pattern is found to be dominated by a narrow peak centered a function halo angle. The amount of polarization in this peak is much higher than expected from Fresnel at the alone. The observations are explained with a birefringence–diffraction halo polarization model. refraction of the hexagonal face of the halo-generating crystals is found to be 41 and 54 μm for two The effective diameter separate scans. An independent single-wavelength parhelion observation indicates a stronger birefringence in an even smaller angular scattering range and a crystal diameter of 220 μm. Crystal sizes peak concentrated derived from the halo intensity distributions are found to be consistent with those obtained from polarization. The data demonstrate the power of halo polarimetry as a tool for detection and identification of birefringent crystals in terrestrial or extraterrestrial atmospheres.

References

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a The 22° halo angles were calculated using the indices of refraction of ice given by Hobbs23 which are valid with respect to vacuum and a given are the mean for ordinary and extraordinary refraction. P is the degree of polarization; its temperature of −3°C. The halo angles by photon statistics. (Px)zero and (Py)zero are the instrumental zero-point polarizations in the second and standard deviation is determined in degrees of polarization. The plane of reference is the scattering plane. Data for the polarimetric camera third Stokes parameters expressed are also included.

aEquation (17) is used to transform Px. into the second Stokes parameter Q. A is the polarized intensity of the maximum height of the birefringence peak, C is the residual polarization, and QB and IB are the background in Q and the background intensity, respectively. UB is the background in the third Stokes parameter U obtained by averaging the Py values. All the parameters, A, C, QB, UB, and IB, are measured with respect to the maximum halo intensity (IH)max. θh is the halo angle and θ1/2 is the angular separation between the maximum of the diffraction peak and its half-value point. The last column gives the results of a χ2 test. The number of points is 38 for scan A and 23 for scan B.

Table III

Polarization of the Background Intensity on Which the Halo Signal is Superposeda

Wavelength (nm)

Px × 104

Py × 104

Psc × 104

Pvert × 104

402

−27 ± 7

−56 ± 6

−142 ± 19

127 ± 14

441

−28 ± 8

−48 ± 6

−126 ± 20

109 ± 14

481

−13 ± 7

−40 ± 7

−95 ± 21

91 ± 14

622

29 ± 7

−22 ± 4

−16 ± 15

50 ± 8

712

47 ± 7

−16 ± 3

14 ± 13

36 ± 6

791

53 ± 7

−14 ± 4

24 ± 15

32 ± 8

850

3 ± 17

15 ± 6

37 ± 29

−34 ± 12

a The Stokes parameters are expressed in degree of polarization. Px and Py are the second and third Stokes parameters divided by the intensity; the plane of reference is the scattering plane. In the last column, the polarization has been decomposed on a nonorthogonal basis consisting of the scattering plane and the celestial vertical. The resulting parameters are Psc and Pvert. This decomposition separates one particular type of multiple scattering from the others (see text).

a The 22° halo angles were calculated using the indices of refraction of ice given by Hobbs23 which are valid with respect to vacuum and a given are the mean for ordinary and extraordinary refraction. P is the degree of polarization; its temperature of −3°C. The halo angles by photon statistics. (Px)zero and (Py)zero are the instrumental zero-point polarizations in the second and standard deviation is determined in degrees of polarization. The plane of reference is the scattering plane. Data for the polarimetric camera third Stokes parameters expressed are also included.

aEquation (17) is used to transform Px. into the second Stokes parameter Q. A is the polarized intensity of the maximum height of the birefringence peak, C is the residual polarization, and QB and IB are the background in Q and the background intensity, respectively. UB is the background in the third Stokes parameter U obtained by averaging the Py values. All the parameters, A, C, QB, UB, and IB, are measured with respect to the maximum halo intensity (IH)max. θh is the halo angle and θ1/2 is the angular separation between the maximum of the diffraction peak and its half-value point. The last column gives the results of a χ2 test. The number of points is 38 for scan A and 23 for scan B.

Table III

Polarization of the Background Intensity on Which the Halo Signal is Superposeda

Wavelength (nm)

Px × 104

Py × 104

Psc × 104

Pvert × 104

402

−27 ± 7

−56 ± 6

−142 ± 19

127 ± 14

441

−28 ± 8

−48 ± 6

−126 ± 20

109 ± 14

481

−13 ± 7

−40 ± 7

−95 ± 21

91 ± 14

622

29 ± 7

−22 ± 4

−16 ± 15

50 ± 8

712

47 ± 7

−16 ± 3

14 ± 13

36 ± 6

791

53 ± 7

−14 ± 4

24 ± 15

32 ± 8

850

3 ± 17

15 ± 6

37 ± 29

−34 ± 12

a The Stokes parameters are expressed in degree of polarization. Px and Py are the second and third Stokes parameters divided by the intensity; the plane of reference is the scattering plane. In the last column, the polarization has been decomposed on a nonorthogonal basis consisting of the scattering plane and the celestial vertical. The resulting parameters are Psc and Pvert. This decomposition separates one particular type of multiple scattering from the others (see text).